noise_block {kDGLM}

noise_block

Description

Creates the structure for a Noise block. This block represents an independent random noise that should be added to the linear predictor. The variance of the noise cannot be formally estimated, as such we use a discount strategy similar to that of West and Harrison (1997) to specify it.

Usage

noise_block(..., name = "Noise", D = 0.99, R1 = 0.1, H = 0)

Arguments

...

Named values for the planning matrix.

name

String: An optional argument providing the name for this block. Can be useful to identify the models with meaningful labels, also, the name used will be used in some auxiliary functions.

D

scalar or vector: A sequence of values specifying the desired discount factor for each time. It should have length 1 or t, where t is the size of the series. If both D and H are specified, the value of D is ignored.

R1

scalar: The prior variance of the noise.

H

scalar: The variance of the noise. If both D and H are specified, the value of D is ignored.

Details

For the details about the implementation see dos Santos et al. (2024).

For the details about dynamic regression models in the context of DLMs, see West and Harrison (1997), chapters 6 and 9.

Value

A dlm_block object containing the following values:

• FF Array: A 3D-array containing the regression matrix for each time. Its dimension should be n x k x t, where n is the number of latent states, k is the number of linear predictors in the model and t is the time series length.

• FF.labs Matrix: A n x k character matrix describing the type of value of each element of FF.

• G Matrix: A 3D-array containing the evolution matrix for each time. Its dimension should be n x n x t, where n is the number of latent states and t is the time series length.

• G.labs Matrix: A n x n character matrix describing the type of value of each element of G.

• D Array: A 3D-array containing the discount factor matrix for each time. Its dimension should be n x n x t, where n is the number of latent states and t is the time series length.

• H Array: A 3D-array containing the covariance matrix of the noise for each time. Its dimension should be the same as D.

• a1 Vector: The prior mean for the latent vector.

• R1 Matrix: The prior covariance matrix for the latent vector.

• var.names list: A list containing the variables indexes by their name.

• order Positive integer: Same as argument.

• n Positive integer: The number of latent states associated with this block (2).

• t Positive integer: The number of time steps associated with this block. If 1, the block is compatible with blocks of any time length, but if t is greater than 1, this block can only be used with blocks of the same time length.

• k Positive integer: The number of outcomes associated with this block. This block can only be used with blocks with the same outcome length.

• pred.names Vector: The name of the linear predictors associated with this block.

• monitoring Vector: The combination of monitoring, monitoring and monitoring.pulse.

• type Character: The type of block (Noise).

References

Mike West, Jeff Harrison (1997). Bayesian Forecasting and Dynamic Models (Springer Series in Statistics). Springer-Verlag. ISBN 0387947256.

Junior, Silvaneo Vieira dos Santos, Mariane Branco Alves, Helio S. Migon (2024). “kDGLM: an R package for Bayesian analysis of Dynamic Generialized Linear Models.”

See Also

fit_model

Other auxiliary functions for structural blocks: TF_block(), block_mult(), block_rename(), block_superpos(), harmonic_block(), intervention(), polynomial_block(), regression_block(), specify.dlm_block(), summary.dlm_block()

Examples

noise_block(mu = 1, D = 0.99, R1 = 1e-2)